SOLUTION: Assume 𝛼 is opposite side a, 𝛽 is opposite side b, and 𝛾 is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triang

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Question 1204422: Assume 𝛼 is opposite side a, 𝛽 is opposite side b, and 𝛾 is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth. (If not possible, enter IMPOSSIBLE.)
𝛼 = 119°,
a = 13,
b = 27
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

if
°,
,


since °, use the Law of Cosines equation:








using quadratic formula, we get following solutions:

or


so, there is no real solution for side
For () theorem with ° () and , there are solutions and !

answer: IMPOSSIBLE

Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!

IMPOSSIBLE FROM THE START. NO CALCULATION NECESSARY. Why? Because the longest
side of a triangle is always opposite the largest angle.  is obtuse and
would have to be the largest angle in the triangle if there were one. But, as 
we see, the side opposite α, "a", at only 13, is NOT the longest side, for
the side b, opposite angle β, is longer, at 27.

Edwin
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